Chern-Simons theory and atypical Hall conductivity in the Varma phase

TL;DR

This paper investigates the topological properties and anomalous Hall effect in a fermionic Lieb lattice model, revealing a unique Chern-Simons response linked to relativistic pseudospin-0 quasiparticles.

Contribution

It introduces a novel analysis of the topological response in a Lieb lattice fermionic model, connecting the DKP Hamiltonian to an emergent Chern-Simons theory and atypical Hall conductivity.

Findings

Identification of a topological Varma phase with broken time-reversal symmetry

Derivation of the Landau-level spectrum for DKP quasiparticles

Observation of an atypical quantum Hall effect in the model

Abstract

In this letter, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gauge field, we calculate both the Landau-level spectrum and the emergent Chern-Simons theory. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice.